Image texture not showing on object that has UV Map?
I think what the tutorial left out was, that before painting on your target, you have to assign the resulting (at first probably blank) texture to a material and then switch into a view that supports textured display. 
Either solid with textures enabled, Material Preview or Render Preview.

The Texture Properties are supposed to set the image properties before it is used as a brush. It does not effect the resulting texture directly.

Back in Blender 2.7x and before you could assign textures to UVs without using materials. That only worked with BI and could be pretty confusing, so they removed the functionality. 
If you have the node wrangler addon enabled, you can have your material nodes open somewhere and CTRL SHIFT click on a texture node to preview it in the viewport.